nbininv

Negative binomial inverse cumulative distribution function

Syntax

X = nbininv(Y,R,P)

Description

X = nbininv(Y,R,P) returns
the inverse of the negative binomial cdf with corresponding number
of successes, R and probability of success in a
single trial, P. Since the binomial distribution
is discrete, nbininv returns the least integer X such
that the negative binomial cdf evaluated at X equals
or exceeds Y. Y, R,
and P can be vectors, matrices, or multidimensional
arrays that all have the same size, which is also the size of X.
A scalar input for Y, R, or P is
expanded to a constant array with the same dimensions as the other
inputs.

The simplest motivation for the negative binomial is the case
of successive random trials, each having a constant probability P of
success. The number of extra trials you must
perform in order to observe a given number R of
successes has a negative binomial distribution. However, consistent
with a more general interpretation of the negative binomial, nbininv allows R to
be any positive value, including nonintegers.

Examples

How many times would you need to flip a fair coin to have a
99% probability of having observed 10 heads?

flips = nbininv(0.99,10,0.5) + 10
flips =
33

Note that you have to flip at least 10 times to get 10 heads.
That is why the second term on the right side of the equals sign is
a 10.

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